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For a line array immersed in a stationary homogeneous noise field composed of plane waves of differing speeds and angles of arrival, standard beamforming is not useful for estimating the noise spectrum directionality. However, the two-dimensional spectrum of the received noise field enables resolution in temporal-frequency and in spatial-frequency and can thereby indicate the temporal-frequency content and the apparent speed along the line array of plane-wave arrivals. The interrelationships and attributes of the space-time correlation, the cross-spectrum, and the two-dimensional spectrum are presented and interpreted via simple examples. A technique for estimation of the two-dimensional spectrum for a sparse line array and examples of its use and interpretation are given.
Nuttall et al. (Wed,) studied this question.